I want to check if my data are normally distributed, in order to decide if performing either a parametric (ANOVA) or non parametric test to check differencies among means.
1) Should I test the normality of each group separately or pool all the data together?
2) The sofwere I am using (SIGMAPLOT) does perform automatically a normality test (Shapiro-Wilk) when asked to do ANOVA and return a single P value (so I guess it pools all the data together). Does it make any sense?
Considering that if my experimental groups result to be actually different, the distribution of my data pooled together may result distributed around 2 different means (so not normal), I think the correct way should be to test the normality in each group separately.
What do you think?
Thanks
Hi Katia,
You should test normality in each group separately.. (unfortunately I have never worked in SigmaPlot to help you more).
Hello Katia,
Normally, one would fit the model, find the residuals for all cases (observed DV score - estimated/predicted/fitted DV score), and test that batch of (error) scores for fit to a normal distribution. That would yield a single test result. I can't tell you whether sigmaplot is doing just that (the right way), or simply taking all of the observed DV values across groups and evaluating their fit to a normal distribution (the wrong way).
If you want to focus on the observed DV scores, then Radek Pileček 's recommendation to evaluate these separately by group is preferred to lumping the scores into a single batch (with possible multi-modal shape!) and evaluating that. You will, of course, have to run k goodness-of-fit tests (k = number of groups) instead of one.
Good luck with your work.
The by group and use residuals are appropriate if you think NHST is helpful for deciding whether the deviation from normality is large enough to be concern (it probably isn't, at least on its own). To get a feel for whether the within group deviation for normality is of a large magnitude, it is useful to plot a qq normal test (no idea what Sigma Plot command that is, but Wilkinson I'm put it in there), and plot the separate lines for each. This provides extra information about the assumptions since differences in the slopes of the lines show show heterogeniety.
The value of all of these things depend on the sample size. Also, are there transformation that are appropriate for the data, what Mosteller and Tukey called the ladder of re-expression.
- Badges
- Science topic
- Similar topics
- Cognitive Science
- Thinking